helehex / moplex

Generalized complex numbers for Mojo🔥

Moplex🔥

Complex types for Mojo🔥

Mojo version 24.2

Moplex provides generalized complex numbers for the mojo programming language.

Complex numbers have a real and imaginary part which can be added, multiplied, and exponentiated.

5 + 4i

The imaginary part multiplied by itself is -1

i*i = -1

Generalized Complex

Moplex also has Paraplex numbers (also called dual numbers), and Hyperplex numbers (also called hyperbolic numbers)

In Moplex, all three of these type are considered the unital hybrids, and the imaginary part is considered the antiox

They are similar to complex, in that the antiox also squares to a real number:

Paraplex numbers, written like 3+1o, has an antiox that squares to zero -> o*o = 0

Hyperplex numbers, written like 1+2x, have an antiox that squares to one -> x*x = 1

You can in fact make a number which has an antiox that squares to any real by parameterizing the Hybrid type.

This looks like: HybridInt[-2](0,1), which squares to -2

Multiplex

When adding two HybridSIMD types with differing antiox squares, it will result in a Multiplex type

Example: (1 + 1i) + (2 + 2o) = (3 + 1i + 2o)

Using in Mojo

to import and use a type, you can do:

from moplex import moprint, Complex64, Paraplex64, Hyperplex64, HybridInt, i, o, x

moprint(Complex64(-1,-2)**i)
moprint(Paraplex64(1,1) + o)
moprint(Hyperplex64(8,6) * x)
moprint(Complex64(-1,-2) + Paraplex64(1,1) + Hyperplex64(8,6))

You can also import just the antiox parts, but they dont sum together yet due to them being HybridIntLiteral type.

(only MultiplexSIMD for now)

This may change with future updates.